-/* @(#)e_jn.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
+ * software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
-#if defined(LIBM_SCCS) && !defined(lint)
-static char rcsid[] = "$NetBSD: e_jn.c,v 1.9 1995/05/10 20:45:34 jtc Exp $";
-#endif
-
/*
* __ieee754_jn(n, x), __ieee754_yn(n, x)
* floating point Bessel's function of the 1st and 2nd kind
* of order n
- *
+ *
* Special cases:
* y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
* y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
* yn(n,x) is similar in all respects, except
* that forward recursion is used for all
* values of n>1.
- *
+ *
*/
#include "math.h"
#include "math_private.h"
-#ifdef __STDC__
static const double
-#else
-static double
-#endif
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */
-#ifdef __STDC__
static const double zero = 0.00000000000000000000e+00;
-#else
-static double zero = 0.00000000000000000000e+00;
-#endif
-#ifdef __STDC__
- double __ieee754_jn(int n, double x)
-#else
- double __ieee754_jn(n,x)
- int n; double x;
-#endif
+double __ieee754_jn(int n, double x)
{
int32_t i,hx,ix,lx, sgn;
- double a, b, temp, di;
+ double a, b, temp=0, di;
double z, w;
/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
ix = 0x7fffffff&hx;
/* if J(n,NaN) is NaN */
if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x;
- if(n<0){
+ if(n<0){
n = -n;
x = -x;
hx ^= 0x80000000;
x = fabs(x);
if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */
b = zero;
- else if((double)n<=x) {
+ else if((double)n<=x) {
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
if(ix>=0x52D00000) { /* x > 2**302 */
- /* (x >> n**2)
+ /* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Let s=sin(x), c=cos(x),
+ * Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
*
* n sin(xn)*sqt2 cos(xn)*sqt2
case 3: temp = cos(x)-sin(x); break;
}
b = invsqrtpi*temp/sqrt(x);
- } else {
+ } else {
a = __ieee754_j0(x);
b = __ieee754_j1(x);
for(i=1;i<n;i++){
}
} else {
if(ix<0x3e100000) { /* x < 2**-29 */
- /* x is tiny, return the first Taylor expansion of J(n,x)
+ /* x is tiny, return the first Taylor expansion of J(n,x)
* J(n,x) = 1/n!*(x/2)^n - ...
*/
if(n>33) /* underflow */
}
} else {
/* use backward recurrence */
- /* x x^2 x^2
+ /* x x^2 x^2
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
* 2n - 2(n+1) - 2(n+2)
*
- * 1 1 1
+ * 1 1 1
* (for large x) = ---- ------ ------ .....
* 2n 2(n+1) 2(n+2)
- * -- - ------ - ------ -
+ * -- - ------ - ------ -
* x x x
*
* Let w = 2n/x and h=2/x, then the above quotient
* To determine how many terms needed, let
* Q(0) = w, Q(1) = w(w+h) - 1,
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
- * When Q(k) > 1e4 good for single
- * When Q(k) > 1e9 good for double
- * When Q(k) > 1e17 good for quadruple
+ * When Q(k) > 1e4 good for single
+ * When Q(k) > 1e9 good for double
+ * When Q(k) > 1e17 good for quadruple
*/
/* determine k */
double t,v;
* single 8.8722839355e+01
* double 7.09782712893383973096e+02
* long double 1.1356523406294143949491931077970765006170e+04
- * then recurrent value may overflow and the result is
+ * then recurrent value may overflow and the result is
* likely underflow to zero
*/
tmp = n;
if(sgn==1) return -b; else return b;
}
-#ifdef __STDC__
- double __ieee754_yn(int n, double x)
+/*
+ * wrapper jn(int n, double x)
+ */
+#ifndef _IEEE_LIBM
+double jn(int n, double x)
+{
+ double z = __ieee754_jn(n, x);
+ if (_LIB_VERSION == _IEEE_ || isnan(x))
+ return z;
+ if (fabs(x) > X_TLOSS)
+ return __kernel_standard((double)n, x, 38); /* jn(|x|>X_TLOSS,n) */
+ return z;
+}
#else
- double __ieee754_yn(n,x)
- int n; double x;
+strong_alias(__ieee754_jn, jn)
#endif
+
+double __ieee754_yn(int n, double x)
{
int32_t i,hx,ix,lx;
int32_t sign;
- double a, b, temp;
+ double a, b, temp=0;
EXTRACT_WORDS(hx,lx,x);
ix = 0x7fffffff&hx;
if(n==1) return(sign*__ieee754_y1(x));
if(ix==0x7ff00000) return zero;
if(ix>=0x52D00000) { /* x > 2**302 */
- /* (x >> n**2)
+ /* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Let s=sin(x), c=cos(x),
+ * Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
*
* n sin(xn)*sqt2 cos(xn)*sqt2
b = __ieee754_y1(x);
/* quit if b is -inf */
GET_HIGH_WORD(high,b);
- for(i=1;i<n&&high!=0xfff00000;i++){
+ for(i=1;i<n&&high!=0xfff00000;i++){
temp = b;
b = ((double)(i+i)/x)*b - a;
GET_HIGH_WORD(high,b);
}
if(sign>0) return b; else return -b;
}
+
+/*
+ * wrapper yn(int n, double x)
+ */
+#ifndef _IEEE_LIBM
+double yn(int n, double x) /* wrapper yn */
+{
+ double z = __ieee754_yn(n, x);
+ if (_LIB_VERSION == _IEEE_ || isnan(x))
+ return z;
+ if (x <= 0.0) {
+ if(x == 0.0) /* d= -one/(x-x); */
+ return __kernel_standard((double)n, x, 12);
+ /* d = zero/(x-x); */
+ return __kernel_standard((double)n, x, 13);
+ }
+ if (x > X_TLOSS)
+ return __kernel_standard((double)n, x, 39); /* yn(x>X_TLOSS,n) */
+ return z;
+}
+#else
+strong_alias(__ieee754_yn, yn)
+#endif
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